ANALYSIS OF CRACK-TIP SINGULARITIES FOR AN INTERFACIAL PERMEABLE CRACK IN METAL/PIEZOELECTRIC BIMATERIALS

By modeling metal as a special piezoelectric material with extremely small piezoelectricity and extremely large permittivity, we have obtained the analytical solutions for an interracial permeable crack in metal/piezoelectric bimaterials by means of the generalized Stroh formalism. The analysis shows that the stress fields near a permeable interracial crack tip are usually with three types of singularities： r^-1/2±iε and r^-1/2. Further numerical calculation on the oscillatory index ε are given for 28 types of metal/piezoelectric bimaterials combined by seven commercial piezoelectric materials： PZT-4, BaTiO3, PZT-5H, PZT-6B, PZT-7A, P-7 and PZT-PIC 151 and four metals： copper, silver, lead and aluminum, respectively. The explicit expressions of the crack tip energy release rate （ERR） and the crack tip generalized stress intensity factors （GSIF） are obtained. It is found that both the ERR and GSIF are independent of the electric displacement loading, although they seriously depends on the mechanical loadings.

两种材料的性质对双材料界面裂纹能量释放率及应力强度因子的影响

在实际工程中,结构往往是由多种材料构成,而裂纹经常在两种材料的界面上扩展。针对双材料界面裂纹,建立相应的计算模型。用能量释放率来描述裂纹的扩展情况,并根据界面裂纹能量释放率解析计算方法对不同的材料性质、外荷载、构件厚度,以及裂纹两侧不同的材料宽度对裂纹扩展时的能量释放率和应力强度因子进行仿真分析,得到了能量释放率和两种材料的弹性模量、外荷载及构件厚度之间的关系变化的曲线,以及裂纹两侧不同的材料宽度和应力强度因子之间的关系。并对界面裂纹和单一材料裂纹的情况进行分析、比较。

压电压磁双层材料界面二维裂纹分析

该文利用积分变换和奇异积分方程技术研究压电压磁双材料界面裂纹二维断裂问题。假设界面上压电材料电势和压磁材料磁势为零;压电层表面受机械载荷和电位移作用,压磁层表面受机械载荷和磁导作用。导出了相应问题的应力强度因子和机械能量释放率的表达式,给出了机械能量释放率的数值结果。结果表明:在同样机械载荷作用下,压电压磁双材料界面裂纹要比相应的弹性双材料不易产生和(或)传播,而且增加层的高度可以抑制裂纹扩展。研究结果对多层电磁复合结构的设计具有理论与应用价值。